Find an equation of variation where y varies directly as x and y=580 and when x=180?

Question

This question is driving me NUTS!! I know the equation to solve these is y=k.x so you end up with 580 over 180 so what do I do from here do I actually divide 580 and 180 or do I reduce? It's really annoying because sometimes the answers are fractions and sometimes decimals! AHHH! Anyways I get y=3.2x

Answer 1

Don't stress over this. You are on the right track. The reason you keep getting a fractional and a decimal answer is because they are the same number, just expressed differently. And yes, it is okay to reduce your fraction. I will do this in just a moment, as you shall see.

Find the value of k. If y = kx, then k = y/x = 580/180 = 29/9 ~ 3.22. Now plug this value for k into your equation to get y = 3.22 x or y = (29/9) x. They are the same equation since 3.22 closely approximates 29/9.